Systems and methods for designing a high-precision narrowband digital filter for use in a communications system with high spectral efficiency

ABSTRACT

Systems and methods for transmitting information at very high data rates through narrowband communication channels are provided. The systems and methods involve modulating a message signal with a novel return-to-zero, abrupt phase modulation technique and filtering the modulated signal with a sophisticated high-precision digital filter. The digital filter is designed based on fractal modeling of the frequency spectrum of the modulated signal. The systems and methods of the present invention enable data rates exceeding 5 Mbps to be delivered through frequency channels as narrow as 50 KHz under a variety of channel conditions.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional PatentApplication No. 60/626,212 entitled “USM (Generic, Symmetrical andAsymmetrical)” filed on Nov. 8, 2004, and U.S. Patent Applicationentitled “Systems and Methods for High-Efficiency Transmission ofinformation Through Narrowband Channels,” filed concurrently herewith onJun. 29, 2005, patent application Ser. No. 11/171,177, the entiredisclosure of each of which is incorporated herein by reference.

FIELD OF THE INVENTION

This invention relates generally to the transmission of informationthrough communication channels. More specifically, this inventionprovides systems and methods for transmitting information at very highdata rates through narrowband communication channels using a novelmodulation scheme and sophisticated high-precision digital filtering.

BACKGROUND OF THE INVENTION

Advances in communications technologies, combined with the widespreadadoption of personal communication devices (“PCSs”), have revolutionizedthe way information is disseminated and shared. Information can now bedelivered directly to computer desktops, laptops, personal digitalassistants (“PDAs”), cellular telephones, digital music players, andother portable devices over wired or wireless connections, providing avirtually unlimited connection experience for all users. In particular,the rapid expansion of wireless technologies has fueled the demand forfaster and more efficient wireless transmission of voice, data, andvideo on a global basis.

Information is transmitted over a wireless channel from an informationsource to a destination by means of a wireless communications system,such as the conventional system shown in FIG. 1. At its simplest form,wireless communications system 100 includes: (1) modulator 105; (2)transmitter 110; (3) wireless channel 115; (4) receiver 120; and (5)demodulator 125. Modulator 105 processes the information into a formsuitable for transmission over wireless channel 115. The information maybe in the form of voice, data, audio, imagery, video, or any other typeof content conveyed in an information signal, also referred to as amessage signal. Modulator 105 essentially translates the message signalinto a modulated signal suitable for transmission over wireless channel115 by modifying one or more characteristics of a carrier signal. Themodulated signal is passed on to wireless channel 115 by transmitter110, which usually filters and amplifies the modulated signal prior toits transmission. The function of wireless channel 115 is to provide awireless link or connection between the information source anddestination. Once transmitted through wireless channel 115, themodulated signal is detected and amplified by receiver 120 to take intoaccount any signal attenuations introduced during transmission bywireless channel 115. Finally, the transmitted signal is demodulated bydemodulator 125 so as to produce a close estimate of the originalmessage signal.

The performance of a wireless communications system such as wirelesscommunications system 100 is, in part, dictated by the performance ofits modulator, e.g., modulator 105. For it is the modulator that isresponsible for converting the message signal into a signal suitable fortransmission so as to maximize the use of the overall system resources.For example, a high performance modulator should generate a modulatedsignal having a frequency spectrum that, when filtered and transmittedby a transmitter such as transmitter 110, would utilize only a smallfraction of the total channel bandwidth, thereby enabling many users toshare the channel bandwidth simultaneously. A high performance modulatorshould also work in conjunction with a high performance filter in thetransmitter to ensure optimal preservation of the frequency spectrum ofthe modulated signal.

Current wireless communications systems use many different modulationtechniques, including, but not limited to, amplitude shift keying(“ASK”), frequency shift keying (“FSK”), binary phase shift keying(“BPSK”), quadrature phase shift keying (“QPSK”) and its variations,minimum shift keying (“MSK”) and Gaussian minimum shift keying (“GMSK”),among others. These modulation techniques are digital techniques inwhich the message signal is represented by a sequence of binary symbols.Each symbol may have one or more bits, depending on the modulationtechnique used.

Typically, these modulation techniques switch or key the amplitude,frequency, and/or phase of a carrier signal according to the binarysymbols in the message signal, e.g., according to binary symbols “0” and“1.” For example, different amplitudes are used to represent both binarysymbols in ASK, different frequencies are used to represent both binarysymbols in FSK, and different phases are used to represent both binarysymbols in BPSK. QPSK is a variation of BPSK in which two bits or moreare used per symbol. The phase of the carrier takes on one of fourequally spaced values, such as 0, π/2, π, and 3π/2, with each valuecorresponding to a unique symbol, e.g., 00, 10, 11, and 01. MSK and GMSKare variations of FSK in which the change in carrier frequency from onebinary symbol to another is half the bit rate of the message signal.

The selection of a digital modulation technique for use in a wirelesscommunications system depends on several factors. A desirable digitalmodulation technique provides low bit error rates at low signal-to-noiseratios, occupies a minimum bandwidth, performs well in the presence ofmultipath and fading conditions, and is cost-effective to implement.Depending on the physical characteristics of the channel, requiredlevels of performance and target hardware trade-offs, some modulationtechniques will prove to be a better fit than others. Consideration mustbe given to the required data rate, acceptable level of latency,available bandwidth, and target hardware cost, size, and powerconsumption. For example, in personal communication systems that serve alarge subscriber community, the cost and complexity of the receiversmust be minimized. In this case, a modulation technique that is simpleto detect is most attractive. In cellular systems where intersymbolinterference is a major issue, the performance of the modulationtechnique in an interference environment is extremely important.

The performance of a modulation technique is often measured in terms ofits power efficiency and bandwidth efficiency. Power efficiencydescribes the ability of a modulation technique to preserve thefidelity, i.e., an acceptable bit error probability, of the messagesignal at low power levels. In digital communication systems, higherfidelity requires higher signal power. The amount by which the signalpower should be increased to obtain a certain level of fidelity dependson the type of modulation employed. The power efficiency of a digitalmodulation technique is a measure of how favorably this tradeoff betweenfidelity and signal power is made, and is often expressed as the ratioof the signal energy per bit to noise power spectral density required atthe receiver input for a certain probability of error.

Bandwidth efficiency describes the ability of a modulation technique toaccommodate data within a limited bandwidth. In general, increasing thedata rate implies decreasing the pulse-width of a digital symbol, whichincreases the bandwidth of the signal. Bandwidth efficiency reflects howefficiently the allocated bandwidth is utilized. Bandwidth efficiency isdefined as the ratio of the throughput data rate per Hertz in a givenbandwidth. The system capacity of a digital modulation technique isdirectly related to the bandwidth efficiency of the modulationtechnique, since a modulation technique having a greater bandwidthefficiency will transmit more data in a given spectrum allocation.

In general, modulation techniques trade bandwidth efficiency for powerefficiency. For example, FSK is power efficient but not as bandwidthefficient and QPSK and GMSK are bandwidth efficient but not as powerefficient. Since most wireless systems are bandwidth limited due tofrequency spectrum allocations, modulation techniques that concentratetheir performance on bandwidth efficiency are generally preferable. Infact, most wireless communication standards available today use morebandwidth-efficient modulation techniques such as QPSK and itsvariations, in use by the PHS and PDC Japanese standards, and IS-54 andIS-95 American standards, and GMSK, in use by the GSM global standard.

The bandwidth efficiencies achieved by the digital modulation techniquescurrently adopted by the wireless standards are, however, only in theorder of 1-10 bps/Hz. Such bandwidth efficiencies are not able tosatisfy the rapidly rising demand for faster and more efficient wirelessservices that are capable of serving a large number of userssimultaneously.

To address these concerns, two new sets of modulation techniques havebeen developed: (1) spread spectrum modulation techniques; and (2)narrowband modulation techniques. Spread spectrum modulation is atechnique in which the modulated signal bandwidth is significantly widerthan the minimum required signal bandwidth. Bandwidth expansion isachieved by using a function that is independent of the message andknown to the receiver. The function is a pseudo-noise (“PN”) sequence orPN code, which is a binary sequence that appears random but can bereproduced in a deterministic manner by the receiver. Demodulation atthe receiver is accomplished by cross-correlation of the received signalwith a synchronously-generated replica of the wide-band PN carrier.

Spread spectrum modulation has many features that make it particularlyattractive for use in wireless systems. First and foremost, spreadspectrum modulation enables many users to simultaneously use the samebandwidth without significantly interfering with one another. The use ofPN codes allows the receiver to separate each user easily even thoughall users occupy the same spectrum. As a result, spread spectrum systemsare very resistant to interference, which tends to affect only a smallportion of the spectrum and can be easily removed through filteringwithout much loss of information. Additionally, spread spectrum systemsperform well in the presence of multipath fading and Doppler spread.

The main disadvantage of spread spectrum systems is that they are verybandwidth inefficient for a single user or a single wireless cell, sincethe bandwidth utilized is much more than that necessary fortransmission. In fact, bandwidth efficiency for a single user is so lowthat most spread spectrum systems report bandwidth efficiency for thewhole channel, to emphasize their ability to simultaneously serve manyusers with the available channel bandwidth. In addition, spread spectrumsystems are also much more complex than systems employing traditionalmodulation techniques, thereby increasing overall system design,deployment, and maintenance costs.

Narrowband modulation techniques, such as those described in U.S. Pat.Nos. 5,930,303, 6,748,022, and 6,445,737, provide an entirely differentapproach. Instead of spreading the signal over a wide bandwidth range tooptimize the number of users sharing the channel bandwidthsimultaneously, narrowband modulation techniques attempt to squeeze thefrequency spectrum into a as narrow of a band as possible in order tomaximize both the bandwidth efficiency for an individual user and theoverall channel utilization for a large number of users. In thenarrowband modulation techniques described therein, phase reversalsoccurring before, in the middle, at the end, or after a bit period areused to generate a modulated signal having most of its energyconcentrated in a very narrow peak centered at a carrier frequency. Asmost of the signal energy is concentrated in the narrow peak,transmission of the modulated signal may be accomplished by transmissionof the narrow peak, thereby significantly improving the bandwidthefficiency for an individual user.

While achieving bandwidth efficiencies of 30-60 bps/Hz, these narrowbandmodulation techniques are not very practical because they require theuse of a specialized analog crystal filter with a resonant frequencytuned by a shunt capacitor. Such a filter is very difficult to implementin practice due to tuning imperfections of the shunt capacitor,irregularities of the crystal material employed, and other challengesassociated with designing high-precision analog crystal filters.Furthermore, these narrowband modulation techniques are very susceptibleto intersymbol interference, may not perform well under high bit errorrates, and require higher transmission power than traditional modulationtechniques such as FSK and BPSK.

Because currently-available modulation techniques have not been able toachieve high bandwidth and power efficiencies while performing wellunder various channel conditions, broadband wireless services that reacha large number of users simultaneously have not yet been fully deployed.Such services should be able to serve users with voice, data, audio,imagery, and video at high data rates and low infrastructure costs toservice providers and consumers alike. Such services should also be ableto optimize the number of users served by better utilization of theallocated frequency spectrum.

In view of the foregoing, there is a need in this art for a digitalmodulation technique that achieves very high bandwidth efficiency undervarious channel conditions.

There is a further need in this art for a high-precision narrowbanddigital filter for use in conjunction with a narrowband digitalmodulation technique in a communications system that achieves highbandwidth efficiency when transmitting information through narrowbandcommunication channels.

There is also a need in this art for a communications system thatoptimizes bandwidth utilization when providing wireless services to alarge number of users simultaneously under various channel conditions.

SUMMARY OF THE INVENTION

In view of the foregoing, a general object of the present invention isto provide a digital modulation technique that achieves very highbandwidth efficiency under various channel conditions.

In one aspect, the present invention provides a high-precisionnarrowband digital filter for use in conjunction with a narrowbanddigital modulation technique in a communications system that achieveshigh bandwidth efficiency when transmitting information throughnarrowband communication channels.

In another aspect, the present invention provides a communicationssystem that optimizes bandwidth utilization when providing wirelessservices to a large number of users simultaneously under various channelconditions.

These and other aspects of the present invention are accomplished byproviding communications systems and methods that are characterized bytheir bandwidth efficiency, high data rates and enhanced data capacity.The communications system and methods of the present invention employ anovel narrowband digital modulation technique in conjunction with ahigh-precision digital filter to achieve broadband-like services withina narrow frequency spectrum.

The novel narrowband digital modulation technique of the presentinvention, hereinafter referred to as Ultra Spectral Modulation (“USM”)technique, comprises a return-to-zero modulation technique that usesabrupt phase changes to represent incoming binary symbols in a modulatedsignal, herein referred to as a “USM-modulated signal.” In oneembodiment, the abrupt phase changes occur mid-pulse, i.e., in themiddle of a bit period, after an integer number of cycles of the carriersignal. In an exemplary embodiment, a binary symbol, e.g., “0” or “1”,is represented with an integer number of cycles, e.g., n cycles, of acarrier signal, of which n/2 cycles are used at a given phase and theother n/2 cycles are used at a phase shift, with the abrupt phase shiftoccurring mid-pulse. In one embodiment, the USM-modulated signal has adouble-sideband suppressed carrier (“DSSC”) frequency spectrum with twowide spectrum sidebands and no carrier.

The USM technique represents all the information in the message signalwith the abrupt phase shifts occurring in the USM-modulated signal. Thatis, all the information conveyed in the message signal may be recoveredby knowing where the phase shifts occur or by preserving the positionsof the phase shifts during transmission. As a result, transmission maybe accomplished by transmitting only a narrow band of frequenciesrequired for identifying the phase shifts, i.e., by transmitting only aportion of one or both sidebands in the USM-modulated signal within anarrow band of frequencies.

The present invention also provides a high-Q, low-tolerancesophisticated digital filter that is able to preserve the positions ofthe phase shifts in a very narrow band of frequencies. Filtering theUSM-modulated signal with the digital filter designed according to theprinciples and embodiments of the present invention and describedhereinbelow produces a filtered signal with a time response thataccurately identifies where the abrupt phase shifts in the USM-modulatedsignal occur.

In a preferred embodiment, the digital filter may be designed byselecting a center frequency and a bandwidth based on unique fractalbifurcation patterns occurring on the frequency spectrum of aUSM-modulated signal. The USM technique of the present inventionproduces a USM-modulated signal having a unique DSSC frequency spectrumthat may be modeled with fractal bifurcation patterns or a set offractal primitives.

In a preferred embodiment, the fractal bifurcation patterns are selectedso as only a narrow band of frequencies need be transmitted. As aresult, narrowband transmission of information may be accomplished sinceonly a narrow band of frequencies of the message signal may betransmitted at any desired data rate. In one exemplary embodiment, thewireless communications systems and methods of the present invention areable to transmit 5 Mbps in a very narrow 50 KHz channel.

Transmission of a USM-modulated signal may be accomplished by two uniquetransmitter approaches: (1) a fractal-based transmitter filteringapproach; and (2) a fractal-based look-up table transmitter approach. Inthe fractal-based transmitter filtering approach, the high-Q,low-tolerance digital filter is designed based on the selection of afractal bifurcation index and a given data rate desired fortransmission. The digital filter is used to filter the USM-modulatedsignal prior to transmission through a communications channel.

In the fractal-based table look-up approach, the USM-modulated signal istransmitted through use of a simple look-up table storing samplesextracted from the fractal modeling of the frequency spectrum of thefiltered USM-modulated signal and used to represent a binary symbol,e.g., a “0” or a “1.” Transmission of a binary symbol is accomplished bysimply encoding the symbol into its corresponding samples stored in thelook-up table.

Accordingly, two unique receiver approaches may be used in conjunctionwith either one of the two unique transmitter approaches to recover thetransmitted signal: (1) a fractal-based receiver filtering approach; and(2) a fractal-based spectral estimator receiver approach. In thefractal-based receiver filtering approach, a receiver filter designedaccording to the fractal bifurcation index and the desired transmissiondata rate is used to extract the transmitted signal. The clock isrecovered and used to phase lock the receiver clock, which is thensynchronized with the transmitted signal. A demodulator including acorrelator, a phase detector, and a decision block is then used torecover the transmitted signal.

In the fractal-based spectral estimator receiver approach, a spectralestimator is used to recover the spectrum of the transmitted signal. Aspectral selector is used to select the transmitted frequencies in therecovered spectrum. A demodulator including a correlator, a phasedetector, and a decision block is then used to recover the transmittedsignal.

The present invention also provides a unique transmitter/receiverpolarization approach suitable for satellite communications. Thesatellite communications system makes use of horizontally polarized andvertically polarized antennas to transmit and detect USM-modulatedsignals. The satellite transmitter includes a signal generator foradapting a USM-modulated signal for transmission through the polarizedantennas. The satellite receiver detects the transmitted signal by meansof a spectral estimator or a fractal-based receiver filter, a referencephase lock loop, a spectral selector, and other receiver circuitry.

Advantageously, the communications systems and methods of the presentinvention enable data rates exceeding 5 Mbps to be delivered throughfrequency channels as narrow as 50 KHz under a variety of channelconditions. The communications system and methods of the presentinvention may operate as a standalone network or be integrated intoexisting wireless systems at very low overhead costs. In addition, thecommunications system and methods of the present invention enablewireless service providers to provide broadband wireless services to alarge number of users simultaneously by accessing a fully-utilizedfrequency spectrum that may be divided into various channels of verynarrow bandwidths.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects of the present invention will beapparent upon consideration of the following detailed description, takenin conjunction with the accompanying drawings, in which like referencecharacters refer to like parts throughout, and in which:

FIG. 1 is an exemplary schematic diagram of a conventional wirelesscommunications system;

FIG. 2 is an exemplary diagram of a message signal and a USM-modulatedsignal according to the principles and embodiments of the presentinvention;

FIG. 3 is an exemplary diagram of a USM-modulated signal and itsfrequency spectrum according to the principles and embodiments of thepresent invention;

FIG. 4 is an exemplary diagram showing a USM-modulated signal and thefiltered USM-modulated signal filtered with a filter designed accordingto the principles and embodiments of the present invention;

FIG. 5 is an exemplary diagram of a magnified frequency spectrum of aUSM-modulated signal according to the principles and embodiments of thepresent invention;

FIGS. 6A-B are exemplary diagrams of two sets of fractal primitives formodeling the frequency spectrum of a USM-modulated signal according tothe principles and embodiments of the present invention;

FIG. 7 is an exemplary fractal bifurcation tree generated according tothe principles and embodiments of the present invention;

FIG. 8 is an exemplary modeled frequency spectrum generated by adding aset of fractal primitives according to the principles and embodiments ofthe present invention;

FIG. 9 is an exemplary schematic diagram showing the selection of afilter bandwidth and center frequency according to a fractal bifurcationtree;

FIG. 10 is an exemplary graph of a filter bandwidth selected accordingto the principles and embodiments of the present invention versus afractal bifurcation index for a given desired data rate;

FIG. 11 is an exemplary graph showing the capacity of a communicationssystem designed according to the principles and embodiments of thepresent invention versus a fractal bifurcation index;

FIG. 12 is an exemplary plot showing the frequency response of a high-Q,low tolerance, linear-phase digital filter designed according to theprinciples and embodiments of the present invention;

FIG. 13 is an exemplary schematic diagram of a communicationstransmitter system using the fractal-based transmitter filteringapproach to transmit message signals through a communications channelaccording to the principles and embodiments of the present invention;

FIG. 14 is an exemplary schematic diagram of a communicationstransmitter system using the fractal-based look-up table transmitterapproach to transmit message signals through a communications channelaccording to the principles and embodiments of the present invention;

FIG. 15 is an exemplary schematic diagram of a communications receiversystem using the fractal-based receiver filtering approach to recovermessage signals transmitted through a communications channel accordingto the principles and embodiments of the present invention;

FIG. 16 is an exemplary plot showing the frequency response of a high-Q,low tolerance, linear-phase digital receiver filter superimposed withthe frequency response of a high-Q, low tolerance, linear-phase digitaltransmitter filter designed according to the principles and embodimentsof the present invention;

FIG. 17 is an exemplary schematic diagram of a demodulator for use withthe communications receiver system shown in FIG. 15;

FIG. 18 is an exemplary plot showing a reference signal to be used in amatched filter according to the principles and embodiments of thepresent invention;

FIG. 19 are exemplary plots of signals generated by a second orderCostas decision loop for use in a communications receiver systemaccording to the principles and embodiments of the present invention;

FIG. 20 is an exemplary schematic diagram of a communications receiversystem using the fractal-based spectral estimator receiver approach torecover message signals transmitted through a communications channelaccording to the principles and embodiments of the present invention;

FIG. 21 is an exemplary embodiment of a communications system designedaccording to the principles of the present invention;

FIG. 22 is another exemplary embodiment of a communications systemdesigned according to the principles of the present invention;

FIG. 23 is another exemplary embodiment of a communications systemdesigned according to the principles of the present invention;

FIG. 24 is yet another exemplary embodiment of a communications systemdesigned according to the principles of the present invention;

FIG. 25 is an exemplary embodiment of a satellite communications systemdesigned according to the principles of the present invention; and

FIG. 26 is yet another exemplary embodiment of a satellitecommunications system designed according to the principles of thepresent invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Generally, the present invention provides communication systems andmethods for transmitting information through narrowband communicationchannels. Information, as used herein, may be in the form of voice,data, audio, imagery, video, or any other type of content conveyed in aninformation signal, also referred to as a message signal. The messagesignal represents information by means of binary symbols, with eachsymbol having one or more bits.

Message signals according to the present invention are modulated priorto transmission through a communications channel. A channel, as usedherein, may be any communications channel, including a wired channel,e.g., cable, or a wireless channel. In general, modulation refers to theprocess by which information conveyed in the message signal is encodedin a carrier signal to generate a modulated signal. Typically, theencoding involves modifying one or more characteristics of the carriersignal according to the binary symbols in the message signal. A carriersignal may be any analog signal of a given frequency, for example, asinusoidal wave at 100 KHz. A modulated signal, as used herein, refersto the carrier signal that has been modified according to the messagesignal.

The modulated signal has a frequency spectrum representation comprisingits frequency components. Modulated signals according to the ultraspectrum modulation (“USM”) technique of the present invention havefrequency spectrums comprising no carrier and two bands or “sidebands”of frequencies, one above (the “upper sideband” or “USB”) and one below(the “lower sideband” or “LSB”) the carrier frequency. Transmission ofone of the sidebands is referred to as single-sidebandsuppressed-carrier (“SSSC”) transmission and transmission of bothsidebands is referred to as double-sideband suppressed carrier (“DSSC”)transmission.

Transmission of the modulated signal through a communications channelmay first be accomplished by filtering the modulated signal to extractthe necessary frequencies. Accordingly, the modulated signal may befiltered by an analog or digital filter. In one embodiment, themodulated signal is filtered by a linear-phase digital filter asdescribed hereinbelow. A filter, as used herein, is any device, process,or algorithm for limiting the spectrum of a signal to a given band offrequencies. The band of frequencies is generally referred to as thebandwidth of the filter.

The bandwidth of the channel refers to the band of frequencies allocatedfor transmission of one or more modulated signals. For example, achannel having a bandwidth of 100 MHz supports the transmission of oneor more modulated signals within a frequency spectrum of 100 MHz. If,for example, each modulated signal is filtered down to a bandwidth of 10KHz, then the channel is able to support the transmission of 10,000 suchsignals. The amount of data that can be transferred in a channel havinga given bandwidth is referred to as the channel's data rate andexpressed in bits per second. The maximum data rate supported by achannel for a given bandwidth, noise level, and other channelassumptions is referred to as the channel capacity and given by theShannon-Hatley theorem.

Aspects of the invention further provide for the fractal modeling ofsidebands using fractal bifurcation patterns or fractal primitives. Afractal, as used herein, is a geometric object with a self-similarstructure that occurs at different levels of magnification. A fractalcan be generated by a repeating pattern, in a typically recursive oriterative process. The repeating pattern may be referred to as a fractalprimitive, or simply, as a fractal bifurcation pattern. A fractalbifurcation pattern is a geometric object that may be bifurcated anumber of times to generate smaller, self-similar patterns at differentscales or levels of detail. The number of bifurcations is given by afractal bifurcation index.

The present invention further provides for the design of a digitalfilter, transmitter and receiver based on fractal modeling of sidebands.A digital filter may be designed based on a fractal bifurcation indexand a desired data rate as described hereinbelow to transmit a modulatedsignal modulated with the USM technique. The USM-modulated signal mayalso be transmitted by using a fractal-based look-up table, with entriesgenerated according to the fractal modeling of the sidebands of aUSM-modulated signal. Different alternative embodiments of receivers fordemodulating the transmitted modulated signal and recovering theoriginal message signal are also described hereinbelow. It will furtherbe appreciated that as new and different modulation techniques, filterdesign approaches, and transmitter and receiver circuitry are developedsuch modulation techniques, filter design approaches, and transmitterand receiver circuitry may also be accommodated by the presentinvention.

I. Ultra Spectral Modulation

Ultra Spectral Modulation (“USM”) comprises a return-to-zero modulationtechnique that uses abrupt phase changes in a carrier signal torepresent incoming binary symbols. The abrupt phase changes occurmid-pulse, i.e., in the middle of a bit period, after an integer numberof cycles of the carrier signal, or at a bit boundary. In an exemplaryembodiment, a binary symbol, e.g., “0” or “1”, is represented with aninteger number of cycles, e.g., n cycles, of a carrier signal, of whichn/2 cycles are used at a given phase and the other n/2 cycles are usedat a phase shift, with the abrupt phase shift occurring mid-pulse. Themodulated carrier signal is referred to herein as the “USM-modulatedsignal.”

Referring to FIG. 2, an exemplary schematic diagram of a message signaland a USM-modulated signal according to the principles and embodimentsof the present invention is described. Message signal 200 is a signalrepresented by the following binary sequence: “010010.” Message signal200 is modulated using the USM technique of the present invention into asinusoidal carrier having a given carrier frequency, which in this caseis four cycles per pulse-width. For example, if a pulse representing asingle bit lasts one second, then the carrier frequency would be 4 Hz,i.e., 4 cycles in one second. Alternative, if the carrier frequency isset at, for example, 20 MHz, a carrier signal with four cycles perpulse-width or four cycles per bit would result in a data rate of 5Mbps.

Using USM to modulate message signal 200 with a sinusoidal carrierhaving a carrier frequency at least twice of the data rate producesmodulated signal 205. Modulated signal 205 is a sinusoidal wave havingabrupt phase shifts every mid-pulse. Each bit is represented with twosinusoidal patterns, a “data bit” pattern lasting for the first half ofthe pulse-width, e.g., for the first two cycles of the carrierfrequency, and a “datum bit” pattern lasting for the second half of thepulse-width, e.g., for the last two cycles of the carrier frequency.

A data bit pattern for a given binary digit, e.g., “0” or “1,” has aphase that is 180° degrees away from the phase of the datum bit pattern.Additionally, a data bit pattern for a given binary digit has a phasethat is 180° degrees away from the phase of the data bit pattern of theother binary digit. For example, as illustrated, a data bit pattern fora “0” bit has a phase of θ while the datum bit pattern for the “0” bithas a phase of θ−π. Conversely, a data bit pattern for a “1” bit has aphase of θ−π while the datum bit pattern for the “1” bit has a phase ofθ.

The main characteristic of the USM technique lies in the abrupt phaseshifts occurring mid-pulse. The abrupt phase shifts may be viewed asanother layer of phase reversals occurring on top of traditional BPSKmodulation techniques, in which phase shifts occur only at the bittransitions, i.e., at the edge of each pulse. Having the datum bitpattern inserted in each pulse ensures a return-to-zero modulationtechnique with a DSSC frequency spectrum, i.e., without energy in thecarrier frequency, as described hereinbelow.

It should be understood by one skilled in the art that the carriersignal, carrier frequency, and phase values used to modulate a signalaccording to the USM technique may all be selected as desired. Further,it should be understood by one skilled in the art that the abrupt phaseshifts may be of π+/−φ degrees, where φ is any phase value between 0 and180 degrees. It should also be understood by one skilled in the art thatthe phase of the data bit pattern for the “0” bit may be selected asdesired, with the corresponding data bit pattern for the “1” bit being aphase shift away.

The use of the USM technique results in a DSSC modulated signal having afrequency spectrum containing two wide spectrum sidebands and nocarrier. Referring now to FIG. 3, an exemplary schematic diagram of aUSM-modulated signal and its frequency spectrum according to theprinciples and embodiments of the present invention are described.Modulated signal 300 is represented in the frequency domain by frequencyspectrum 305. Frequency spectrum 305 has two main symmetric sidebands,upper sideband 310 and lower sideband 315, which are respectively aboveand below carrier frequency 320 at 20 MHz. Upper sideband 310 extends to30 MHz, while lower sideband 320 extends to 10 MHz, thereby resulting ina USM-modulated signal bandwidth of 20 MHz.

Since the sidebands are symmetric, transmission of both sidebands is notrequired. A message signal may be USM-modulated and transmitted in aSSSC system, that is, transmitted with a single sideband. However, sincethe USM technique represents all the information in the message signalwith the abrupt phase shifts occurring in the USM-modulated signal, allthe information conveyed in the message signal may be recovered byknowing where the phase shifts occur or by preserving the positions ofthe phase shifts during transmission. That is, if the phase shifts areknown, the original message signal can be recovered. For example, asillustrated in FIG. 2, knowing the initial phase of the USM-modulatedsignal corresponds to a “0,” the positions of the phase shifts everymid-pulse, and the occurrence of a phase shift at the beginning of apulse when there is continuity in the bit pattern conveys enoughinformation for a receiver to be able to recover the original messagesignal.

As a result, transmission may be accomplished by transmitting only anarrow band of frequencies required for identifying the phase shifts,i.e., by transmitting only a portion of one or both sidebands in theUSM-modulated signal within a narrow band of frequencies. TheUSM-modulated signal may therefore be filtered with a very sharpnarrowband filter as described hereinbelow that preserves the abruptphase shifts in the USM-modulated signal and attenuates the otherfrequency components. Because the phase shifts are abrupt, i.e.,occurring at once with an immediate change in phase, the sudden shift inphase is reflected in the wide spectrum sidebands that may be filteredout by a narrowband filter as described hereinbelow to produce afiltered USM-modulated signal that ramps up and down according to thephase shifts. The ramping up and down in the filtered USM-modulatedsignal is a result of the return-to-zero USM technique.

Referring now to FIG. 4, an exemplary diagram showing a USM-modulatedsignal and the filtered USM-modulated signal filtered with a filterdesigned according to the principles and embodiments of the presentinvention is described. USM-modulated signal 400 is filtered out by anarrowband filter to generate filtered USM-modulated signal 405. Thenarrowband filter used to generate filtered USM-modulated signal 405 hasa given center frequency and a given bandwidth that were selected bysimulation to produce the desired result of accurately preserving theabrupt phase shifts in the USM-modulated signal within a band as narrowas possible. As described hereinbelow, the center frequency andbandwidth of the narrowband filter may be selected based on fractalmodeling of the frequency spectrum of USM-modulated signal 400. Doing soensures an even more accurate filtering process, that is, an even moreaccurate positioning of the abrupt phase shifts occurring inUSM-modulated signal 400.

As illustrated, abrupt phase shifts occurring in USM-modulated signal400 determine peaks or valleys in filtered USM-modulated signal 405,which ramps up and down according to the abrupt phase shifts. Forexample, abrupt phase shift 410 in USM-modulated signal 400 results in apeak in filtered USM-modulated signal 405 while abrupt phase shift 415in USM-modulated signal 400 results in a valley in filteredUSM-modulated signal 405.

It should be understood by one skilled in the art that the narrowbandfilter must be carefully chosen in order to accurately capture theposition of the phase shifts in the USM-modulated signal. As describedhereinbelow, it will be appreciated that the narrowband filter must be ahigh-Q, low tolerance, linear-phase filter with a very sharp passband,very sharp transition bands, and very sharp stopbands. In oneembodiment, the filter is designed to have a passband ripple of no morethan 0.1 dB and a uniform stopband attenuation of at least 60 dB. Such afilter is designed based on fractal modeling of the frequency spectrumof a USM-modulated signal.

Modulating a signal with the USM technique of the present inventionproduces a USM-modulated signal having a unique DSSC frequency spectrum.The unique feature of the frequency spectrum is that the abrupt phaseshifts occurring mid-pulse result in sidebands that have repeatingself-similar spectral lines that may be modeled using fractalbifurcation patterns or fractal primitives. Referring now to FIG. 5, anexemplary schematic diagram of a magnified frequency spectrum of aUSM-modulated signal according to the principles and embodiments of thepresent invention is described.

Frequency spectrum 500 has two main sidebands that are symmetric aroundthe carrier frequency. The symmetry of the sidebands is reflected in theself-similar patterns A1-A2, B1-B2, and C1-C2. These self-similarpatterns are modeled with fractal primitives, as described hereinbelow,and aid in the selection of a center frequency and a filter bandwidthfor the narrowband filter of the present invention.

II. Fractal Modeling of Sidebands

The self-similar patterns present in frequency spectrum 500 shown inFIG. 5 may be modeled using a set of fractal bifurcation patterns orfractal primitives. Referring now to FIGS. 6A-B, exemplary diagrams oftwo sets of fractal primitives for modeling the frequency spectrum of aUSM-modulated signal according to the principles and embodiments of thepresent invention are described. Fractal primitive 600 in FIG. 6A is abifurcating fractal primitive with a trapezoidal shape. Fractalprimitive 614 in FIG. 6B is a bifurcating fractal primitive with anarch-like shape. Fractal primitives 600 and 614 may be generated by anyfractal pattern generator capable of generating fractals, such asvarious fractal pattern generators implemented as software routines. Forexample, a Moire or Mandelbrot fractal pattern generator as implementedin the art with Java™ or Matlab™ may be used to generate fractalpatterns.

Both fractal primitives 600 and 614 have two symmetric bifurcations, aninner bifurcation and an outer bifurcation, that may be furtherbifurcated to generate additional bifurcations at different scales,resolutions, or levels of detail. The bifurcation process can be thoughtof in terms of a “fractal bifurcation tree,” with each level of the treerepresenting a different scale, resolution, or level of detail. The rootof the tree corresponds to the original fractal primitive, e.g., fractalprimitive 600 in FIG. 6A or fractal primitive 614 in FIG. 6B.

At each subsequent level in the fractal bifurcation tree, eachbifurcation generates an additional fractal primitive that has the exactsame structure as its originating fractal primitive, except that it isat a lower scale or higher resolution. Each outer bifurcation in the newfractal primitive is centered at the outer edges of its previousbifurcation. For example, bifurcating fractal primitive 600 generatesfractal primitives 602 and 604, with the same structure as fractalprimitive 600 and with the outer bifurcations of fractal primitives 602and 604 centered at the outer edges of fractal primitive 600. Similarly,bifurcating fractal primitive 614 generates fractal primitives 616 and618, with the same structure as fractal primitive 614 and with the outerbifurcations of fractal primitives 616 and 618 centered at the outeredges of fractal bifurcation 614.

Each bifurcation step is indexed with an integer, referred to herein asthe “fractal bifurcation index.” The fractal bifurcation index indicatesthe scale, level of detail, or depth within the fractal bifurcationtree. At each scale or level in the fractal bifurcation tree, there are2^(N) fractal primitives, where N is the fractal bifurcation index. Forexample, N=0 denotes the root or start of the fractal bifurcation treewith original fractal primitives 600 (FIG. 6A) and 614 (FIG. 6B). AtN=1, there are two fractal primitives, 602-604 at FIGS. 6A and 616-618at FIG. 6B. At N=2, there are four fractal bifurcations, 606-612 atFIGS. 6A and 620-626 at FIG. 6B.

Referring now to FIG. 7, an exemplary fractal bifurcation tree generatedaccording to the principles and embodiments of the present invention isdescribed. Fractal bifurcation tree 700 is shown at a depth or fractalbifurcation index of 5, i.e., at 5 different scales or levels of detail.Each vertical line beyond the tree root corresponds to one fractalprimitive generated off fractal primitive 705. At each level of thetree, twice the fractal primitives in the previous level, i.e., 2^(N)fractal primitives, are generated. For example, at N=1, there are twofractal primitives, i.e., fractal primitives 710-715. At N=2, there arefour fractal primitives, i.e., fractal primitives 720-735.

It will be appreciated that each fractal primitive can be thought of astwo sidebands around a particular frequency. For example, fractalprimitive 705 can be thought of as a very rough modeled representationof the sidebands of a USM-modulated signal. A modeled frequency spectrumthat more closely resembles or approximates the sidebands of aUSM-modulated signal may therefore be generated by using a set offractal primitives at different levels of detail.

Fractal primitives, such as fractal primitives 600 (FIG. 6A) and 614(FIG. 6B), can be used to model the frequency spectrum of aUSM-modulated signal by first selecting a desired modeling accuracy,i.e., selecting how close the modeled frequency spectrum should be tothe original frequency spectrum, and determining a correspondingbifurcation index required to achieve the desired accuracy. The modeledfrequency spectrum may then be generated by adding all fractalbifurcations at all levels of the fractal bifurcation tree.

Referring now to FIG. 8, an exemplary modeled frequency spectrumgenerated by adding a set of fractal primitives according to theprinciples and embodiments of the present invention is described.Modeled frequency spectrum 800 was generated by adding, at eachfrequency, a set of fractal bifurcations at a fractal bifurcation indexof N=6. As it can be seen from the figure, the higher the fractalbifurcation index used to generate a modeled frequency spectrum, thehigher the resolution and the closer to the spectrum of theUSM-modulated signal the modeled frequency spectrum would be.

It should be understood by one skilled in the art that centering theouter bifurcations of fractal primitives at a given tree depth at theouter edges of the fractal primitives at the previous tree depth ensuresthat the filtered frequency spectrum will return-to-zero at the carrierfrequency, i.e., 20 MHz for the sinusoidal carrier signal used togenerate USM-modulated signal 300 shown in FIG. 3, and at the lower andupper limits of the USM-modulated signal bandwidth, i.e., at 10 and 30MHz.

III. Fractal-Based Digital Filter Design

It will be appreciated that using a fractal bifurcation tree to modelthe frequency spectrum of a USM-modulated signal may be thought of asdividing the bandwidth of the USM-modulated signal into 2^(N)bifurcations. The USM-modulated signal having modeled frequency spectrum800 shown in FIG. 8 and magnified frequency spectrum 500 shown in FIG. 5was filtered with a digital filter having a given center frequency and agiven bandwidth that were selected by simulation to produce the desiredresult of accurately preserving the abrupt phase shifts in theUSM-modulated signal within a band as narrow band as possible. However,since the frequency spectrum of the USM-modulated signal may be modeledwith the fractal bifurcations as described hereinabove, ahigher-precision digital filter may be designed based on the fractalbifurcations required to achieve the return-to-zero characteristics ofthe frequency spectrum of the USM-modulated signal.

Referring now to FIG. 9, an exemplary schematic diagram showing theselection of a filter bandwidth and center frequency according to afractal bifurcation tree is described. Designing a high-Q, low tolerancenarrowband digital filter to preserve the abrupt phase shifts in aUSM-modulated signal, e.g., USM-modulated signal 400 shown in FIG. 4,starts with the realization that the filter bandwidth may be selected asthe narrow bandwidth needed to model the frequency spectrum of theUSM-modulated signal with the fractal primitives, as illustrated indiagram 900.

This narrow bandwidth is a fraction of the total bandwidth of theUSM-modulated signal. The fraction of the total bandwidth is given bythe division of the frequency spectrum of the USM-modulated signal into2^(N) fractal primitives. That is, the bandwidth of the filter, denotedherein by BWF, may be selected as:

$\begin{matrix}{{BWF} \approx \frac{BW}{2^{N}}} & (1)\end{matrix}$where BW is the total bandwidth of the USM-modulated signal and N is thefractal bifurcation index.

The total bandwidth of the USM-modulated signal may be given, in turn,by a desired data rate for transmission. For example, with the carriersignal used to generate USM-modulated signal 205 of FIG. 2 having 4cycles per pulse-width, the bandwidth of the total modulated signal maybe given by four times the desired data rate, that is:

$\begin{matrix}{{{BWF} \approx \frac{4 \times {DataRate}}{2^{N}}} = \frac{DataRate}{2^{N - 2}}} & (2)\end{matrix}$

The bandwidth of the high-Q, low tolerance narrowband digital filterthat may be used to preserve the abrupt phase shifts in a USM-modulatedsignal may therefore be given as a function of a desired data rate and afractal bifurcation index. Similarly, the center frequency of thedigital filter, denoted herein as F_(F), may be given as a function ofthe desired data rate, fractal bifurcation index and the carrierfrequency F_(C), according to:

$\begin{matrix}{F_{F} \approx {F_{C} \pm {\left( {2^{N} - K} \right)\frac{DataRate}{2^{N - 1}}}}} & (3)\end{matrix}$∀K=2M=1, where M=1:(2^(N−1)), and N≠0.

Accordingly, the capacity of a communications system (given inbits/sec/Hz) that uses the USM-modulation technique of the presentinvention and a high-Q, low tolerance, linear-phase narrowband digitalfilter designed with a bandwidth and center frequency as above totransmit a fraction of a sideband of a USM-modulated signal may be givenby:C=2^(N−2)  (4)

It should be understood by one skilled in the art that Equation (3)described hereinabove gives the values of the center frequency F_(F)within the range of the frequency spectrum from (F_(c)−BWF) to(F_(c)+BWF).

It should also be understood by one skilled in the art that other valuesof F_(F) may exist outside the hereinabove mentioned range based on agiven fractal bifurcation index. For example, if it is desired to selecta center frequency outside the range from (F_(c)−BWF) to (F_(c)+BWF),the value of F_(c) in equation (3) described hereinabove may be set to avalue offset by BWF.

Referring now to FIG. 10, an exemplary graph of a filter bandwidthselected according to the principles and embodiments of the presentinvention versus a fractal bifurcation index for a given desired datarate is described. Graph 1000 shows that the communications system ofthe present invention enables data rates exceeding 5 Mbps to bedelivered through frequency channels as narrow as 50 KHz under a varietyof channel conditions.

Referring now to FIG. 11, an exemplary graph showing the capacity of acommunications system designed according to the principles andembodiments of the present invention versus a fractal bifurcation indexis described. Graph 1100 shows that broadband-like wireless services maybe achieved with the communications system of the present inventionwithin a very narrow frequency spectrum. Transmission of a fraction ofone or two sidebands results in a capacity exceeding 100 bits/second/Hzfor a fractal bifurcation index of 9 and above, far superior than anycurrently-available wireless communication system.

It should be understood by one skilled in the art that selecting a givenfractal bifurcation index is a function of the system design for aparticular application. For example, if it is desired to transmit 100channels in a total bandwidth of 36 MHz, the fractal bifurcation indexmay be chosen to optimize the filter design for a given desired datarate, carrier signal, number of users accessing the channels, and soforth.

It should also be understood by one skilled in the art that the high-Q,low tolerance, linear-phase digital filter designed according to theprinciples and embodiments of the present invention has additionaldesign parameters other than the filter bandwidth and center frequencyselected as above. For example, to achieve a very sharp stopband, thedigital filter may be designed with a uniform stopband attenuation of,for example, at least 60 dB. And to minimize the passband ripple, thefilter may be designed with a passband ripple of no more than 0.1 dB.These stringent filter design conditions may generate digital filtershaving a large number of filter taps. Those filters may be implementedin hardware using specially configured circuit boards. With decreasinghardware costs, such filters may be easily implemented in acost-effective manner.

Referring now to FIG. 12, an exemplary plot showing the frequencyresponse of a high-Q, low tolerance, linear-phase digital filterdesigned according to the principles and embodiments of the presentinvention is now described. Frequency response 1200 of a high-Q, lowtolerance, liner-phase digital filter designed according to theprinciples and embodiments of the present invention is shown with verysharp passbands, transition bands, and stopbands. The passband ripple ofthe digital filter having frequency response 1200 is very small toinsignificant, while the stopband attenuation is very high. Thebandwidth of the digital filter having frequency response 1200 wasdesigned to be around 58.6 KHz and the center frequency was designed atapproximately 47.6 KHz away from the carrier frequency used. Using sucha filter enables the transmission of 5 Mbps within the very narrowbandwidth of the digital filter.

IV. Fractal-Based Transmitter Filtering Approach

Referring now to FIG. 13, an exemplary schematic diagram of acommunications transmitter system using the fractal-based transmitterfiltering approach to transmit message signals through a communicationschannel according to the principles and embodiments of the presentinvention is described. Communications transmitter system 1300 may beused to transmit a message signal according to the principles andembodiments of the present invention by using USM modulator 1305 tomodulate the message signal into a carrier signal and high-Q, lowtolerance, linear-phase digital filter 1310 designed as above, such asthe digital filter having frequency spectrum 1200 shown in FIG. 12, tofilter the USM-modulated signal.

It should be understood by one skilled in the art that additionalfunctional blocks may be present in communications transmitter system1300, such as a channel encoder to introduce redundancy in the messagesignal prior to modulation by USM modulator 1305 and a transmittercircuit having an amplifier to amplify the message signal prior totransmission through a communications channel.

V. Fractal-Based Look-Up Table Transmitter Approach

Referring now to FIG. 14, an exemplary schematic diagram of acommunications transmitter system using the fractal-based look-up tabletransmitter approach to transmit message signals through acommunications channel according to the principles and embodiments ofthe present invention is described. Communications transmitter system1400 may be used to transmit a message signal according to theprinciples and embodiments of the present invention via a simple look-uptable operation. Fractal-based look-up table 1405 is generated bysampling a modeled USM-modulated signal, such as modeled USM-modulatedsignal with modeled frequency spectrum 800 shown in FIG. 8.

Since the frequency spectrum of a USM-modulated signal may be modeledwith fractal bifurcation patterns as described hereinabove, analternative embodiment to transmission of a message signal involvessampling the modeled USM-modulated signal as above and transmitting thesamples through the communications channel. Sampling the modeledUSM-modulated signal is an approximation to sampling a USM-modulatedsignal filtered with a narrowband digital filter, as performed incommunications system 1300 shown in FIG. 13.

Fractal-based look-up table 1405 therefore stores samples extracted fromthe time response counterpart of a modeled frequency spectrum of aUSM-modulated signal. The samples are independent of the USM-modulatedsignal, that is, they may be extracted from the time responsecounterpart of a fractal-modeled frequency spectrum of any USM-modulatedsignal and used in the transmission of any USM-modulated signal.

In one embodiment, fractal-based look-up table 1405 contains two rows ofsamples, with each row corresponding to a different binary symbol, e.g.,“0” or “1.” The samples for each binary symbol are extracted byobserving the modeled frequency spectrum of a USM-modulated signal andnoting which patterns arise as a result of an abrupt phase shiftcorresponding to a “0” or a “1.” Transmission of a binary symbol in amessage signal is accomplished by simply encoding the symbol into itscorresponding samples stored in look-up table 1405.

It should be understood by one skilled in the art that thisfractal-based look-up table transmission approach is very simple andcost-effective to implement, in addition to achieving high data rateswithin a very narrow frequency spectrum. It should also be understood byone skilled in the art that such a system employs high oversampling toreduce the noise in the system and achieve the desired data rateswithout being significantly affected by channel distortions. Forexample, if 32 samples are used for each binary symbol and the carriersignal used has a carrier frequency of 20 MHz, the sampling rate is 160MHz. For a channel of 50 KHz, desired data rates of 5 Mbps and above canstill be achieved.

VI. Fractal-Based Receiver Filtering Approach

Referring now to FIG. 15, an exemplary schematic diagram of a wirelesscommunications receiver system using the fractal-based receiverfiltering approach to recover message signals transmitted through acommunications channel according to the principles and embodiments ofthe present invention is described. Communications receiver system 1500may be used to recover a message signal transmitted according to theprinciples and embodiments of the present invention by first filteringthe transmitted signal with high-Q, low tolerance, linear-phase digitalfilter 1505. Digital filter 1505 is a filter designed based on high-Q,low tolerance, linear-phase digital filter 1310 shown in FIG. 13. Thecenter frequency of digital filter 1310 is selected as a function of acarrier frequency, a fractal bifurcation index and a desired data rateas given in equation (3) described hereinabove. The bandwidth of digitalfilter 1505 is selected as a function of a fractal bifurcation index anda desired data rate with the addition of a small band of frequencies totake into account channel distortions such as fading and inter-symbolinterference, as follows:

$\begin{matrix}{{{BWF} \approx {\frac{4 \times {DataRate}}{2^{N}} \pm \delta}} = {\frac{DataRate}{2^{N - 2}} \pm \delta}} & (5)\end{matrix}$where δ is the small band of frequencies related to a guard band,DataRate is the desired data rate and N is the fractal bifurcationindex.

It should be understood by one skilled in the art that equation (5) isderived from equation (2) above giving the bandwidth of a digitaltransmitter filter, with the addition of the small band of frequenciesδ.

Referring now to FIG. 16, an exemplary plot showing the frequencyresponse of a high-Q, low tolerance, linear-phase digital receiverfilter superimposed with the frequency response of a high-Q, lowtolerance, linear-phase digital transmitter filter designed according tothe principles and embodiments of the present invention is described. Asillustrated in plot 1600, the frequency response of receiver filter 1505is slightly wider than the frequency response of a transmitter filterdesigned as described hereinabove, such as transmitter filter 1310 shownin FIG. 13. The frequency response of receiver filter 1505 also showsthat receiver filter 1505 has slightly smaller passband ripple and aneven sharper stopband than its corresponding transmitter filter, such astransmitter filter 1310 shown in FIG. 13.

Referring back to FIG. 15, once the transmitted signal is filtered byreceiver filter 1505, the transmitter clock is recovered and used tophase-lock the receiver clock by clock detection circuitry 1510. Thephase-locked receiver clock is then used to synchronize communicationsreceiver 1500 with the transmitted signal in order to extract the binarysymbols in the message signal encoded into the abrupt phase shifts inthe transmitted signal. The message signal is recovered by demodulator1515.

Referring now to FIG. 17, an exemplary schematic diagram of ademodulator for use with the communications receiver system shown inFIG. 15 is described. Demodulator 1700 recovers a message signaltransmitted by communications transmitter system 1300 shown in FIG. 13or communications transmitter system 1400 shown in FIG. 14. The firststep towards recovering the message signal is performed by correlator1705, which correlates the phase-locked receiver clock with the filteredtransmitted signal, i.e., with the transmitted signal filtered byreceiver filter 1505 shown in FIG. 15, in order to extract thetransmitted signal at the desired frequencies. Correlator 1705 may beimplemented with any correlator circuitry known to one skilled in theart, including matched filter circuitry.

Referring now to FIG. 18, an exemplary plot showing a reference signalto be used in a matched filter according to the principles andembodiments of the present invention is described. Reference signal 1800is a zero-phase four-cycle sinusoidal wave generated at the centerfrequency selected for the transmitter filter used to transmit a messagesignal for recovery by demodulator 1705, such as transmitter filter 1310shown in FIG. 13 and designed based on the fractal modeling as describedhereinabove. Reference signal 1800 may be used in correlation with thefiltered transmitted signal in blocks of four cycles to generate anoiseless output signal with the same phase as the transmitted signal.

The matched filter employs four-cycle reference signal 1800 in areceiver system for which the corresponding transmitter employs a USMtechnique using four cycles per pulse-width to modulate a binary symbolinto a sinusoidal carrier signal. It should be understood by one skilledin the art that the number of cycles chosen for the sinusoidal referencesignal used by the matched filter may be selected as any number ofcycles that match the number of cycles used by a ultra spectralmodulator when encoding each binary symbol in a message signal within agiven pulse-width.

Referring back to FIG. 17, the phase of the output signal generated bycorrelator 1705 is detected by phase detector 1710, and the detectedphase is then used with the output signal generated by correlator 1705in data bit decision block 1715 to recover the binary symbols encoded inthe transmitted signal, i.e., to recover the message signal. Data bitdecision block 1715 may be implemented with any well-known data bitdecision circuitry to one skilled in the art, including with a Costasdecision loop.

Referring now to FIG. 19, exemplary plots of signals generated by asecond order Costas decision loop for use in a communications receiversystem according to the principles and embodiments of the presentinvention is described. Plot 1900 shows the message signal transmittedwith a communications transmitter system of the present invention, suchas communications transmitter system 1300 shown in FIG. 13 andcommunications transmitter system 1400 shown in FIG. 14. Plot 1905 showsthe frequency response of a Hilbert transform filter used in the Costasloop, and plot 1910 shows the output signal generated by the Costas loopsuperimposed with the message signal recovered by the Costas loop.

As illustrated, the binary symbols of the message signal plotted in plot1900 were correctly recovered by the Costas loop in the output signalplotted in plot 1910. The exemplary Costas loop used to recover thebinary symbols was designed with the following Costas loop parameters:K1=0.1, A=0.16665/4; B=0.01389/16; and F=center frequency of thetransmit filter selected according to equation (3) above. It should beunderstood by one skilled in the art that other parameters may be usedin a Costas loop for recovering message signals transmitted and receivedaccording to the principles and embodiments of the present invention.

VII. Fractal-Based Spectral Estimator Receiver Approach

Referring now to FIG. 20, an exemplary schematic diagram of acommunications receiver system using the fractal-based spectralestimator receiver approach to recover message signals transmittedthrough a communications channel according to the principles andembodiments of the present invention is described. Communicationsreceiver system 2000 may be used to recover a message signal transmittedaccording to the principles and embodiments of the present invention byusing spectral estimator 2005 to estimate the frequency spectrum of thetransmitted signal.

Once the frequency spectrum of the transmitted signal is generated byspectral estimator 2005, spectral selector 2010 is used to extract thetransmitted signal at the desired frequencies, i.e., at the transmittedfrequencies within the narrowband selected for the transmission filterbandwidth according to equation (2) above. The message signal is thenrecovered by demodulator 2020 taking as inputs a phase-locked receiverclock generated by clock detection circuitry 2015 and the transmittedsignals recovered by spectral selector 2010.

It should be understood by one skilled in the art that traditionalspectral estimation, spectral selection, and demodulation circuitry maybe used by communications receiver system 2000. For example, demodulator2020 may be implemented with the correlator, phase detector, and databit decision circuitry of demodulator 1515 shown in FIG. 15 anddescribed above with reference to FIG. 17.

VIII. Communications Systems

It should also be understood by one skilled in the art thatcommunication systems designed according to the principles andembodiments of the present invention may be implemented using anycombination of the communication transmitter and receiver systems shownin FIGS. 13-14, 15, and 20.

Referring now to FIG. 21, an exemplary embodiment of a communicationssystem designed according to the principles of the present invention isdescribed. Communications system 2100 is implemented with communicationstransmitter system 2105 and communications receiver system 2120.Communications transmitter system 2105 is a transmitter system designedusing the fractal-based transmitter filtering approach as describedhereinabove with reference to FIG. 13. Communications receiver system2120 is a receiver system designed using the fractal-based receiverfiltering approach as described hereinabove with reference to FIG. 15.

Referring now to FIG. 22, another exemplary embodiment of acommunications system designed according to the principles of thepresent invention is described. Communications system 2200 isimplemented with communications transmitter system 2205 andcommunications receiver system 2215. Communications transmitter system2205 is a transmitter system designed using the fractal-based look-uptable transmitter approach as described hereinabove with reference toFIG. 14. Communications receiver system 2215 is a receiver systemdesigned using the fractal-based receiver filtering approach asdescribed hereinabove with reference to FIG. 15.

Referring now to FIG. 23, another exemplary embodiment of acommunications system designed according to the principles of thepresent invention is described. Communications system 2300 isimplemented with communications transmitter system 2305 andcommunications receiver system 2320. Communications transmitter system2305 is a transmitter system designed using the fractal-basedtransmitter filtering approach as described hereinabove with referenceto FIG. 13. Communications receiver system 2320 is a receiver systemdesigned using the fractal-based spectral estimator receiver approach asdescribed hereinabove with reference to FIG. 20.

Referring now to FIG. 24, yet another exemplary embodiment of acommunications system designed according to the principles of thepresent invention is described. Communications system 2400 isimplemented with communications transmitter system 2405 andcommunications receiver system 2415. Communications transmitter system2405 is a transmitter system designed using the fractal-based look-uptable transmitter approach as described hereinabove with reference toFIG. 14. Communications receiver system 2405 is a receiver systemdesigned using the fractal-based spectral estimator receiver approach asdescribed hereinabove with reference to FIG. 20.

It should be understood by one skilled in the art that thecommunications systems of FIGS. 21-24 may operate in a standalonewireless network or be integrated into existing wireless standards andsystems at very low overhead costs. In addition, the communicationssystems of FIGS. 21-24 may be used in a variety of communicationsapplications, including in satellite systems with polarized transmitterand receiver antennas.

Further, it should be understood by one skilled in the art that althoughthe systems and methods of the present invention were described withreference to wireless communications, they may also be used in wiredcommunications to achieve broadband-like wired services within a verynarrow frequency spectrum.

IX. Satellite Communications System

Referring now to FIG. 25, an exemplary embodiment of a satellitecommunications system designed according to the principles of thepresent invention is described. Satellite communications system 2500 maybe used in the transmission of signals modulated with the USM techniqueof the present invention. A message signal is first modulated by USMmodulator 2505, using either the fractal-based transmitter filteringapproach or the fractal-based look-up table transmitter approach, andadapted for transmission over horizontally polarized antenna 2515 andvertically polarized antenna 2525 by signal generator block 2510.

The transmitted signal is received at horizontally polarized antenna2520 and vertically polarized antenna 2530. The message signal isrecovered by spectral estimator 2535, reference phase lock loop 2540,time synchronization block 2545, clock detection 2550, spectral selector2555, information decoder 2560, and data bit decision block 2565.

Referring now to FIG. 26, yet another exemplary embodiment of asatellite communications system designed according to the principles ofthe present invention is described. Satellite communications system 2600may be used in the transmission of signals modulated with the USMtechnique of the present invention. A message signal is first modulatedby USM modulator 2605, using either the fractal-based transmitterfiltering approach or the fractal-based look-up table transmitterapproach, and adapted for transmission over horizontally polarizedantenna 2615 and vertically polarized antenna 2625 by signal generatorblock 2610.

The transmitted signal is received at horizontally polarized antenna2620 and vertically polarized antenna 2630. Communications receiversystem 2635 is a receiver system designed using the fractal-basedreceiver filtering approach as described hereinabove with reference toFIG. 15.

The foregoing descriptions of specific embodiments and best mode of thepresent invention have been presented for purposes of illustration anddescription only. They are not intended to be exhaustive or to limit theinvention to the precise forms disclosed. Specific features of theinvention are shown in some drawings and not in others, for purposes ofconvenience only, and any feature may be combined with other features inaccordance with the invention. Steps of the described processes may bereordered or combined, and other steps may be included. The embodimentswere chosen and described in order to best explain the principles of theinvention and its practical application, to thereby enable othersskilled in the art to best utilize the invention and various embodimentswith various modifications as are suited to the particular usecontemplated. Further variations of the invention will be apparent toone skilled in the art in light of this disclosure and such variationsare intended to fall within the scope of the appended claims and theirequivalents.

1. A system for designing a narrowband digital filter for filteringinformation through a communications channel, the digital filtercentered around a center frequency and having a filter bandwidth, thesystem comprising: a modulator for modulating a carrier signal at acarrier frequency with a message signal to generate a modulated signalhaving at least one sideband; and a fractal pattern generator forgenerating a set of fractal bifurcations to model the frequency spectrumof the modulated signal and selecting the center frequency and thefilter bandwidth based on a transmission rate and a fractal bifurcationindex.
 2. The system of claim 1, wherein the modulator comprises anencoder for encoding a first binary symbol into a first portion of thecarrier signal, the first portion of the carrier signal having aninteger number n of cycles and at a first phase, followed by a secondportion of the carrier signal, the second portion of the carrier signalhaving an integer number n of cycles and at a second phase, wherein thesecond phase is at a phase shift away from the first phase.
 3. Thesystem of claim 2, further comprising encoding a second binary symbolinto a third portion of the carrier signal, the third portion of thecarrier signal having an integer number n of cycles and at the secondphase, followed by a fourth portion of the carrier signal, the fourthportion of the carrier signal having an integer number n of cycles andat the first phase.
 4. The system of claim 1, wherein the filterbandwidth is selected based on a desired transmission rate and a fractalbifurcation index.
 5. The system of claim 1, wherein the centerfrequency is selected based on the carrier frequency, a desiredtransmission rate, and the fractal bifurcation index.
 6. The system ofclaim 1, wherein the narrowband digital filter comprises a linear-phasefilter.
 7. The system of claim 1, wherein the narrowband digital filtercomprises a uniform stopband attenuation of at least 60 dB.
 8. Thesystem of claim 1, wherein the narrowband digital filter comprises apassband ripple of no more than 0.1 dB.
 9. A method for designing anarrowband digital filter for filtering information through acommunications channel, the digital filter centered around a centerfrequency and having a filter bandwidth, the method comprising:modulating a carrier signal at a carrier frequency with a message signalto generate a modulated signal having at least one sideband; generatinga set of fractal bifurcations to model the frequency spectrum of themodulated signal; and selecting the center frequency and the filterbandwidth based on a transmission rate and a fractal bifurcation index.10. The method of claim 9, wherein modulating a carrier signal at acarrier frequency with a message signal to generate a modulated signalcomprises encoding a first binary symbol into a first portion of thecarrier signal, the first portion of the carrier signal having aninteger number n of cycles and at a first phase, followed by a secondportion of the carrier signal, the second portion of the carrier signalhaving an integer number n of cycles and at a second phase, wherein thesecond phase is at a phase shift away from the first phase.
 11. Themethod of claim 10, further comprising encoding a second binary symbolinto a third portion of the carrier signal, the third portion of thecarrier signal having an integer number n of cycles and at the secondphase, followed by a fourth portion of the carrier signal, the fourthportion of the carrier signal having an integer number n of cycles andat the first phase.
 12. The method of claim 10, wherein the narrowbanddigital filter comprises a linear-phase filter.
 13. The method of claim10, wherein the narrowband digital filter comprises a uniform stopbandattenuation of at least 60 dB.
 14. The method of claim 10, wherein thenarrowband digital filter comprises a passband ripple of no more than0.1 dB.
 15. A narrowband digital filter for filtering informationthrough a communications channel, the narrowband digital filtercomprising: a filter bandwidth selected based on a transmission rate anda fractal bifurcation index, wherein the fractal bifurcation index isselected by modeling a modulated signal with a set of fractalbifurcations, the modulated signal generated by a modulator whenmodulating a carrier signal at a carrier frequency with a messagesignal; and a center frequency selected based on the carrier frequencyand the fractal bifurcation index.
 16. The narrowband digital filter ofclaim 15, wherein the modulator comprises an encoder for encoding afirst binary symbol into a first portion of the carrier signal, thefirst portion of the carrier signal having an integer number n of cyclesand at a first phase, followed by a second portion of the carriersignal, the second portion of the carrier signal having an integernumber n of cycles and at a second phase, wherein the second phase is ata phase shift away from the first phase.
 17. The narrowband digitalfilter of claim 16, further comprising encoding a second binary symbolinto a third portion of the carrier signal, the third portion of thecarrier signal having an integer number n of cycles and at the secondphase, followed by a fourth portion of the carrier signal, the fourthportion of the carrier signal having an integer number n of cycles andat the first phase.
 18. The narrowband digital filter of claim 16,wherein the narrowband digital filter comprises a linear-phase filter.19. The narrowband digital filter of claim 16, wherein the narrowbanddigital filter comprises a uniform stopband attenuation of at least 60dB.
 20. The narrowband digital filter of claim 16, wherein thenarrowband digital filter comprises a passband ripple of no more than0.1 dB.